Related papers: Stationary iteration methods for solving 3D electr…
In this paper, we will introduce a high order numerical method to solve the scattering problems with non-periodic incident fields and (locally perturbed) periodic surfaces. For the problems we are considering, the classical methods to treat…
A wide variety of (fixed-point) iterative methods for the solution of nonlinear equations (in Hilbert spaces) exists. In many cases, such schemes can be interpreted as iterative local linearization methods, which, as will be shown, can be…
A very simple and efficient local variational iteration method for solving problems of nonlinear science is proposed in this paper. The analytical iteration formula of this method is derived first using a general form of first order…
We develop and analyze the Generalized Multiplicative Gradient (GMG) method for solving a class of convex optimization problems over symmetric cones, where the objective function does not have Lipschitz gradient over the feasible region.…
We present several versions of Regularized Combined Field Integral Equation (CFIER) formulations for the solution of three dimensional frequency domain electromagnetic scattering problems with Perfectly Electric Conducting (PEC) boundary…
This article is the second in a series of two papers concerning the mathematical study of a boundary integral equation of the second kind that describes the interaction of $N$ dielectric spherical particles undergoing mutual polarisation.…
The Helmholtz equation with variable wavenumbers is challenging to solve numerically due to the pollution effect, which often results in a huge ill-conditioned linear system. In this paper, we present a high-order wavelet Galerkin method to…
This paper presents high-order integral equation methods for evaluation of electromagnetic wave scattering by dielectric bumps and dielectric cavities on perfectly conducting or dielectric half-planes. In detail, the algorithms introduced…
We introduce a numerical method that enables efficient modelling of light scattering by large, disordered ensembles of non-spherical particles incorporated in stratified media, including when the particles are in close vicinity to each…
We present a spectral method for solving elliptic equations which arise in general relativity, namely three-dimensional scalar Poisson equations, as well as generalized vectorial Poisson equations of the type $\Delta \vec{N} + \lambda…
In this paper we examine iterative methods for solving the forward ($A{\bf x}={\bf b}$) and adjoint ($A^{T}{\bf y}={\bf g}$) systems of linear equations used to approximate the scattering amplitude, defined by ${\bf g}^{T}{\bf x}={\bf…
Nesterov's well-known scheme for accelerating gradient descent in convex optimization problems is adapted to accelerating stationary iterative solvers for linear systems. Compared with classical Krylov subspace acceleration methods, the…
We solve by Chebyshev spectral collocation some genuinely nonlinear Liouville-Bratu-Gelfand type, 1D and a 2D boundary value problems. The problems are formulated on the square domain $[-1, 1]\times[-1, 1]$ and the boundary condition…
One of the main computational drawbacks in the application of 3-D iterative inversion techniques is the requirement of solving the field quantities for the updated contrast in every iteration. In this paper, the 3-D electromagnetic inverse…
We consider the iterative solution of anisotropic radiative transfer problems using residual minimization over suitable subspaces. We show convergence of the resulting iteration using Hilbert space norms, which allows us to obtain…
We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using…
In many Direct and Inverse Scattering problems one has to use a parameter-fitting procedure, because analytical inversion procedures are often not available. In this paper a variety of such methods is presented with a discussion of…
We study some convergence issues for a recent approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. The approach is based on the minimization on an integral functional which arises from…
In this paper we consider the electromagnetic scattering problem by an obstacle characterised by a Generalized Impedance Boundary Condition in the harmonic regime. These boundary conditions are well known to provide accurate models for thin…
Seismic tomography solves high-dimensional optimization problems to image subsurface structures of Earth. In this paper, we propose to use random batch methods to construct the gradient used for iterations in seismic tomography.…